Corresponding glass-pane railings are known, for example, from DE 20 2007 009 239 U1 or WO 2009/003452 A1. In railings of this type, it is provided to insert the glass panel, which can also consist, for example, of two individual panes which are connected to one another, such as, in particular, adhesively bonded to one another, into a U-shaped profile which holds the glass pane in a clamped manner. The inner walls of said U-shaped profile are of planar configuration. The base region of the glass pane is enclosed by way of a U-shaped profile body made from plastic which is inserted into the U-shaped profile before the mounting of the glass pane. An exact and tilt-resistant alignment of the glass pane takes place subsequently by means of wedge-like inserts. Here, the U-shaped profile body which encloses the base region of the glass pane reaches on both sides of the glass pane as far as into the opening region of the U-shaped profile. Before the glass pane is inserted into the U-shaped profile, said U-shaped profile has already been screwed or welded to a fastening profile which is arranged fixedly on a building. To this end, one of the two limbs of the U-shaped profile can have a bent-over portion, by means of which the U-shaped profile can be hooked onto the fastening profile.